
Men

Women


Exposed cases (n)

100

200

Exposed noncases (n)

400

300

Unexposed cases (n)

400

300

Unexposed noncases (n)

100

200

Risk Ratio

0.25

0.6667

\(\hbox {Pr}(V=v)\)

0.5

0.5

\(\hbox {P}(Y=1 \vert A=0, V=v)\)

0.8

0.6

Weight

0.4

0.3

 Table shows a simple toy example of 2000 subjects, of whom 1000 are exposed to a drug. Here, the covariate V denotes gender, and we assume no unmeasured confounders. The marginal causal risk ratio can be calculated as \(\frac{0.25 \times 0.4 + 0.6667 \times 0.3}{0.4+0.3}=0.428\). Note that the weights are easy to obtain: \(\hbox {Pr}(V=v)\) is just the probability of belonging to the gender, and \(\hbox {P}(Y=1 \vert A=0, V=v)\) is the probability of the outcome among the unexposed in that gender